Adaptive fault clearing scheme for MMC VSC-HVDC grid based on source-grid coordination

ABSTRACT

The invention discloses an adaptive fault clearing scheme for an MMC VSC-HVDC grid based on source-grid coordination. A grid-side circuit breaker topology is disposed at each end of each DC line of the MMC VSC-HVDC grid to coordinate with a source-side control strategy when a fault occurs to the DC line so as to isolate the fault together. When a system runs stably, the voltage regulation controller does not actuate, after the fault occurs, the voltage regulation controller is started, and the output voltage regulation coefficient decreases, so that voltage at outlets of the converters drops accordingly, and coordinates with voltage of the pre-charging capacitor of the grid-side circuit breaker topology to realize fault isolation based on source-grid coordination. The adaptive fault clearing scheme provided by the invention greatly improves the speed of fault isolation.

CROSS REFERENCE TO RELATED APPLICATION

The invention relates to the technical field of VSC-HVDC grid protection and control, in particular to an adaptive fault clearing scheme for an MMC VSC-HVDC grid based on source-grid coordination.

BACKGROUND OF THE INVENTION

As a new generation of power transmission technology, voltage source converter based high voltage direct current transmission (VSC-HVDC) has the advantages of independent control of active power and reactive power, no DC filter and no commutation failure, is available for grid interconnection and large-scale transmission of renewable energy, and is one of the important directions of grid development and reform in the future. The emergence of modular multilevel converters (MMCs) allows VSC-HVDC to develop towards high voltage and high capacity. MMC has become the preferred converter topology for VSC-HVDC systems and has been widely used worldwide.

In long-distance DC transmission projects, overhead lines are the main transmission mode. However, overhead lines are exposed to the external environment and have a high risk of failure. When faults occur in DC grids, the fault current rises rapidly. Due to weak damping properties of DC grids and low tolerance limit of fully-controlled devices, the ability to withstand DC faults is poor. Therefore, the DC grids are required to cut off fault lines quickly within a few milliseconds, thus avoiding harm from the fault current to equipment throughout the grids and ensuring safe and reliable operation of the DC grids.

Fault clearing schemes for DC grids can be divided into source-side schemes and grid-side schemes. With DC buses as boundaries, if a fault clearing scheme requires the coordination of converters and affects external power transmission of converter stations for a short time, the fault clearing scheme can be called a source-side clearing scheme; if a fault clearing scheme only isolates fault lines and does not affect the power transmission of non-fault lines, the fault clearing scheme can be called a grid-side clearing scheme. In the source-side scheme, the fault current is suppressed or turned off by lowering source-side voltage or providing source-side reverse voltage, while in the grid-side scheme, the fault current is suppressed or turned off by increasing line impedance or lowering line voltage.

High controllability of converter stations is utilized in the source-side scheme, but power transmission of converter stations at near-ends of fault lines will be blocked by controlling the fault current through the converter stations during fault clearing, bringing adverse effect to the selectivity. DC circuit breakers are used to clear faults with absolute selectivity in the grid-side scheme, but it is still difficult to develop high-speed DC circuit breakers with high switching capacity due to high costs and difficulties in coordination and control.

SUMMARY OF THE INVENTION

In order to solve technical defects in the prior art, the purpose of the invention is to provide an adaptive fault clearing scheme for an MMC VSC-HVDC grid based on source-grid coordination to achieve fault clearing through source-grid coordination based on a source-side control strategy and a grid-side circuit breaker topology. During a DC fault, the number of sub-modules for the converters is reduced by the control strategy, so that DC voltage at outlets of the converters drops, and adaptively coordinates with voltage of the grid-side pre-charging capacitor to clear the fault.

The purpose is achieved by the following technical solution:

An adaptive fault clearing scheme for an MMC VSC-HVDC grid based on source-grid coordination, wherein the MMC VSC-HVDC grid comprises two source-side converter stations MMC1 and MMC3, two grid-side converter stations MMC2 and MMC4, wherein converters of the four converter stations are connected in a square shape by double-circuit DC overhead lines, and each converter station is equipped with two converters; a grid-side circuit breaker is disposed at each end of each DC line connected with the converters to coordinate with a source-side control strategy when a fault occurs to the DC line so as to isolate the fault together; the grid-side circuit breaker topology comprises:

a steady-state low-loss branch, comprising a disconnector UFD₁, an IGBT device and a disconnector UFD₂ sequentially connected in series;

a transfer branch, comprising a transistor T₀ disposed in parallel, wherein one end of the transistor T₀ is connected with the front end of the disconnector UFD₁, and the other end is connected to a line between the IGBT device and the disconnector UFD₂;

a charging circuit, disposed at the rear ends of the steady-state low-loss branch and the transfer branch and formed by sequentially connecting a pre-charging capacitor C, a switch RCB, a charging resistor R_(C) and a charging inductor L_(C) in series; wherein one end of the pre-charging capacitor C is connected with the rear end of the disconnector UFD₂, and one end of the charging inductor L_(C) is grounded;

a discharging branch, comprising a transistor T₁ connected in parallel with the charging circuit, wherein one end of the transistor T₁ is connected to a ground terminal of the charging inductor L_(C), and the other end is connected to a line between the pre-charging capacitor C and the switch RCB; and

a flyback energy dissipation branch, connected in parallel with the charging circuit and disposed at the rear ends of the charging circuit and the discharging circuit, and comprising a flyback diode D and an energy dissipation resistor R_(e) connected in series; wherein the other end of the energy dissipation resistor R_(e) is grounded, and the other end of the flyback diode D is connected with the rear end of the disconnector UFD₂ and the front end of a current limiting inductor L_(dc) disposed at a terminal;

wherein the source-side control strategy is realized by a voltage regulation controller; when a system runs stably, the voltage regulation controller does not actuate, and the output voltage regulation coefficient K is kept at 1; after a fault occurs, the voltage regulation controller is started, and the output voltage regulation coefficient K decreases within the range of [0,1], so that voltage at outlets of the converters drops accordingly, and coordinates with voltage of the pre-charging capacitor of the grid-side circuit breaker topology to realize fault isolation based on source-grid coordination;

wherein the voltage regulation controller gives corresponding voltage regulation coefficients K at different stages after the fault occurs, and the voltage regulation controller comprises a preliminary current limiting link and an adaptive voltage regulation link; the preliminary current limiting link is put into operation until the system detects the fault, while the adaptive voltage regulation link is put into operation only after the system detects the fault; after the fault occurs, the preliminary current limiting link is started immediately to preliminarily limit the development of fault current; after monitoring the fault, a DC grid protection system switches to the adaptive voltage regulation link, and adaptively coordinates with voltage of the grid-side pre-charging capacitor to isolate the fault together.

The pre-charging capacitor needs to be charged during normal operation of the DC grid, so that the pre-charging capacitor has a rated DC voltage after charging to lower the output voltage by adjusting the number of sub-modules of the converters in the fault isolation stage, and coordinate with voltage of the pre-charging capacitor to decrease and turn off the fault current.

The voltage attenuation speed of the pre-charging capacitor is different at different transition resistance when a fault occurs to the DC grid, and the voltage regulation coefficient K is matched with different transition resistance to adaptively adjust the number of removed sub-modules to cope with both metallic short-circuit faults and high-resistance short-circuit faults.

The pre-charging capacitor C needs to be charged during normal operation of the DC grid, so that the pre-charging capacitor C has a rated DC voltage after charging to lower the output voltage by adjusting the number of sub-modules for the converters in the fault isolation stage, and coordinate with voltage of the pre-charging capacitor C to decrease and turn off the fault current. The voltage attenuation speed of the pre-charging capacitor C is different at different transition resistance when a fault occurs to the DC grid, and the voltage regulation coefficient K is matched with different transition resistance to adaptively adjust the number of removed sub-modules to cope with both metallic short-circuit faults and high-resistance short-circuit faults.

When a fault occurs to the DC grid, fault clearing is achieved by the following steps:

at time t₀, the fault occurs, and fault current flows from the converter stations to a fault point through the steady-state low-loss branch, in the meantime, the preliminary current limiting link is started immediately to preliminarily limit the rise of the fault current, and an instruction is given to block the IGBT device and turn on the thyristor T₀ to allow the fault current on the steady-state low-loss branch to be quickly transferred to the transfer branch; and the disconnector UFD₁ is turned off when the current flowing through the disconnector UFD₁ drops to 0;

at time t₁, the fault is detected, the disconnector UFD₁ is turned off, and the thyristor T₁ is turned on, the pre-charging capacitor C is connected to the fault current circuit, and the number of control sub-modules of the source-side converters is reduced, so that the sum of voltage of sub-modules for upper and lower bridge arms of the converters is less than the voltage u_(Cflt) of the pre-charging capacitor; in the process, the fault current in the transfer branch drops to zero at a large rate to turn off the thyristor T₀, and the fault point is isolated after the thyristor T₀ is turned off;

at time t₂, the thyristor T₀ is turned off, energy of the pre-charging capacitor C is transferred to the current limiting inductor L_(dc), and the disconnector UFD₂ is turned off to isolate the fault line; after the fault is isolated, the MMC switches from an adaptive voltage regulation control mode to a conventional control mode to restore normal operation of the DC grid;

at time t₃, the pre-charging capacitor C is reversely charged, and the current i_(C) of the charging circuit and the current i_(L) of the current limiting inductor L_(dc) start to decrease, in the meantime, the diode D in the flyback energy dissipation branch is turned on, the current i_(D) of the diode D starts to rise from zero, energy of the current limiting inductor L_(dc) is released to the flyback energy dissipation branch, and the pre-charging capacitor C is reversely charged;

at time t₄, the current i_(C) of the charging circuit drops to zero, the thyristor T₁ is turned off, and the current i_(D) of the diode D reaches the maximum value and starts to decrease; and residual energy of the current limiting inductor L_(dc) is gradually released to the flyback energy dissipation branch; and

at time t₅, energy dissipation is over and the fault clearing is completed. Compared with the prior art, the invention has the following positive effects:

Firstly, decoupling of fault isolation and fault energy dissipation is realized, with energy dissipation after isolation, fast isolation and slow energy dissipation, thereby greatly improving the speed of fault isolation, so the adaptive fault clearing scheme is applicable to some working conditions with requirement for rapidity, and has some engineering guiding significance.

Secondly, the grid-side pre-charging capacitor can suppress the fault current and reduce the energy release speed of sub-module capacitors of the MMC, thereby preventing the MMC from failing to fully restore DC voltage immediately after the fault is cleared due to deep discharge, and enhancing the fault ride-through capability of the DC grid.

In addition, the peak value of fault current during a fault is reduced by voltage regulation control, reducing the risk of converter blocking due to overcurrent.

Finally, the voltage attenuation speed of the pre-charging capacitor is different at different transition resistance, and the voltage regulation coefficient can be matched with different transition resistance to adaptively adjust the number of removed sub-modules to cope with both metallic short-circuit faults and high-resistance short-circuit faults.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a topology of a ±500 kV four-terminal MMC DC grid system.

FIG. 2 shows the implementation of adaptive fault clearing based on source-grid coordination and a grid-side circuit breaker topology.

FIG. 3 shows control modes of a preliminary current limiting link and an adaptive voltage regulation link.

FIG. 4 shows a grid-side circuit breaker topology.

FIG. 5 shows a fault equivalent circuit in a preliminary current limiting stage.

FIG. 6 shows a fault equivalent circuit in an adaptive voltage regulation stage.

FIGS. 7a-7c show equivalent circuits in an energy dissipation stage at time t₂-t₃, t₃-t₄ and t₄-t₅, respectively.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention will be further described in detail with reference to accompanying drawings and embodiments. It should be understood that various embodiments described herein are only intended to explain the invention and not to limit the invention.

According to the adaptive fault clearing scheme for an MMC VSC-HVDC grid based on source-grid coordination, the number of sub-modules for the MMC is reduced through a control strategy during a DC fault, so that DC voltage at outlets of the converters drops, and adaptively coordinates with voltage of the grid-side pre-charging capacitor to turn off the fault current and clear the fault.

FIG. 1 shows a topology of a ±500 kV four-terminal MMC DC grid system. A grid-side circuit breaker is disposed on each DC line, as shown in FIG. 2. The grid-side circuit breaker topology shown in FIG. 2 is used to coordinate with the source-side control strategy to clear a fault occurring to the DC line. The grid-side circuit breaker topology can be divided into 5 branches, i.e., a steady-state low-loss branch, a transfer branch, a charging branch, a discharging branch and an energy dissipation branch; wherein the steady-state low-loss branch comprises a disconnector UFD₁, an IGBT device and a disconnector UFD₂ sequentially connected in series; the transfer branch comprises a transistor T₀ disposed in parallel, wherein one end of the transistor T₀ is connected with the front end of the disconnector UFD₁, and the other end is connected to a line between the IGBT device and the disconnector UFD₂; the charging circuit is disposed at the rear ends of the steady-state low-loss branch and the transfer branch and formed by sequentially connecting a pre-charging capacitor C, a switch RCB, a charging resistor R_(C) and a charging inductor L_(C) in series; wherein one end of the pre-charging capacitor C is connected with the rear end of the disconnector UFD₂, and one end of the charging inductor L_(C) is grounded; the discharging branch comprises a transistor T₁ connected in parallel with the charging circuit, wherein one end of the transistor T₁ is connected to a ground terminal of the charging inductor L_(C), and the other end is connected to a line between the pre-charging capacitor C and the switch RCB; and the flyback energy dissipation branch is connected in parallel with the charging circuit and disposed at the rear ends of the charging circuit and the discharging circuit, and comprises a flyback diode D and an energy dissipation resistor R_(e) connected in series; wherein the other end of the energy dissipation resistor R_(e) is grounded, and the other end of the flyback diode D is connected with the rear end of the disconnector UFD₂ and the front end of a current limiting inductor L_(dc) disposed at a terminal.

Due to constrains of voltage resistance and current limitation on power electronic devices, a plurality of thyristors and diodes need to be connected in series or in parallel when a power electronic device does not meet the requirements. Therefore, in the technical solution, the transistor T₀ can be a transistor or the transfer branch formed by connecting more than one transistor in series or in parallel, the transistor T₁ can be a transistor or the discharging branch formed by connecting more than one transistor in series or in parallel, and the flyback diode D can be a flyback diode or the flyback energy dissipation branch formed by connecting more than one flyback diodes in series or in parallel, as the case may be.

As shown in FIG. 2, the grid-side circuit breaker topology has an input side connected to a voltage output side of an MMC voltage regulation controller with an output current i_(dc), an output voltage KU_(dc), and three phases U_(a), U_(b) and U_(c). Each phase comprises an upper bridge arm and a lower bridge arm, both the upper bridge arm and the lower bridge arm comprise KN identical sub-modules SM_(1-N) and bridge arm inductors L_(arm) connected in series. Bridge arm resistors R_(arm), bridge arm inductors L_(arm) and bridge arm resistors R_(arm) are connected in series with N identical sub-modules SM_(1-N). Connecting points of the bridge arm resistors R_(arm) of the upper and lower bridge arms of each phase are connected with the three phases U_(a), U_(b) and U_(c), wherein each sub-module comprises a capacitor C_(SM), two high-power controllable electronic power switches T1 and T2, and two diodes D1 and D2. As shown in FIG. 2, the switches T1 and T2 are inversely connected in parallel with the diodes D1 and D2 respectively, then connected in series, and connected in parallel with the capacitor C_(SM).

The voltage regulation control strategy for converters in different fault stages is given, then the working principle of the MMC DC grid line from fault occurrence to fault clearing is analyzed, and finally the design method of component parameters is given.

By multiplying the number of sub-modules for bridge arm units output by the MMC voltage regulation controller by the voltage regulation coefficient K, the DC voltage at outlets of DC sides of the converters can be K times the rated DC voltage, where the voltage regulation coefficient K is given by the voltage regulation controller, with an operating range of [0,1]. Therefore, in the invention, the following source-side control strategy is given by the MMC voltage regulation controller:

When the system runs stably, the voltage regulation controller does not actuate, and the voltage regulation coefficient K is kept at 1; after a fault occurs, the voltage regulation controller is started, and the voltage regulation coefficient K decreases, so that voltage at outlets of the converters drops accordingly, and coordinates with voltage of the grid-side pre-charging capacitor C to turn off the fault current.

In the invention, the pre-charging capacitor C needs to be charged during normal operation of the DC grid, so that the pre-charging capacitor C has a rated DC voltage after charging to coordinate with the voltage of the pre-charging capacitor in the fault clearing stage, and apply a reverse voltage to the bridge arm inductor to decrease and turn off the fault current.

In the invention, the voltage attenuation speed of the pre-charging capacitor C is different at different transition resistance during a fault, and the voltage regulation coefficient K is matched with different transition resistance to adaptively adjust the number of removed sub-modules to cope with both metallic short-circuit faults and high-resistance short-circuit faults.

Furthermore, in order to realize the voltage regulation control, the invention further provides a voltage regulation controller for realizing the functions. The voltage regulation controller can give corresponding voltage regulation coefficients at different stages after a fault occurs. Specifically, as shown in FIG. 3, the voltage regulation controller comprises two additional control links on the basis of a conventional half-bridge MMC voltage regulation controller, i.e., a preliminary current limiting link and an adaptive voltage regulation link. The preliminary current limiting link is put into operation until the system detects the fault, while the adaptive voltage regulation link is put into operation only after the system detects the fault. After the fault occurs, the preliminary current limiting link works immediately to preliminarily limit the development of fault current; after monitoring the fault, a DC grid protection system switches to the adaptive voltage regulation link, and adaptively coordinates with voltage of the grid-side pre-charging capacitor to clear the fault together.

1) Preliminary Current Limiting Link

The link is put into operation only when a fault is suspected on the line, and the principle is as follows:

The DC-side outlet current i_(dc) of the MMC passes through a differentiation element S to get a DC change rate di_(dc)/dt, the di_(dc)/dt passes through a hysteresis comparator to get an actuating signal, then the di_(dc)/dt is multiplied by a differential coefficient K₁ and the actuating signal to get ΔK_(lim), and finally the ΔK_(lim) is subtracted from the upper limit 1 and passes through a 0-1 limiter to get an output K_(lim) of the preliminary current limiting link, and the K_(lim) is used as the voltage regulation coefficient of the preliminary current limiting link. The hysteresis comparator outputs 1 when the input is greater than the action value and outputs 0 when the input is less than the returned value. When the hysteresis comparator outputs 1, the preliminary current limiting link is started to limit the current, and when the hysteresis comparator outputs 0, the preliminary current limiting link is not started.

During normal operation of the system, the DC line current remains basically constant, and the change rate of the DC current does not exceed the action value of the hysteresis comparator under non-fault disturbance, so the voltage regulation coefficient K=1, and the preliminary current limiting link does not affect the normal operation of the converters. The DC line current rises immediately after a fault occurs, and the voltage regulation coefficient K decreases, so that the DC-side outlet voltage of the converters drops accordingly, preliminarily suppressing the development of the fault current.

2) Adaptive Voltage Regulation Link

In the link, the voltage u_(Cflt) of the grid-side pre-charging capacitor of the fault line is selected as a control signal, and the control signal is divided by the rated voltage U_(dc) of the DC system, then multiplied by a reliability coefficient K_(rel), and subjected to a 0-1 limiting link to obtain an output K_(flt) of the link. With the K_(flt) as the voltage regulation coefficient K, the sum of voltage of sub-modules for MMC bridge arm units is less than u_(Cflt). Since the voltage regulation coefficient K is adaptive to changes in the u_(Cflt), the fault current decreases and is turned off at a large rate.

As shown in FIG. 4, the working principle of the fault clearing scheme is described below in three stages.

1) Charging Stage

At the start of charging, the switch RCB is switched on to connect the charging resistor R_(C) and the charging inductor L_(C) to the charging circuit, then the DC line starts to charge the pre-charging capacitor C. When the capacitor voltage rises to the rated DC voltage, the charging current is zero, then the switch RCB is switched off to isolate the charging branch, and the charging process is finished.

The charging resistor and the charging inductor are configured to suppress the charging speed of the pre-charging capacitor and avoid great impact on the DC system.

The charging process is calculated analytically. Assuming that the DC voltage of the MMC is U_(dc), the voltage of the pre-charging capacitor C is u_(C), and the current of the charging circuit is i_(C), then:

$\begin{matrix} \left\{ \begin{matrix} {{U_{dc} - u_{c} - {L_{c}\frac{di_{C}}{dt}} - {R_{C}i_{C}}} = 0} \\ {{C\frac{{du}_{C}}{dt}} = i_{C}} \end{matrix} \right. & (1) \end{matrix}$

the solution is: i _(C) =D ₁ e ^(αt) cos(βt)+D ₂ e ^(αt) sin(βt)  (2)

where:

$\begin{matrix} \left\{ \begin{matrix} {{D_{1} = {i_{C}\left( \left. 0 \right.\_ \right)}},} & {D_{2} = \frac{{2U_{dc}} - {R_{C}{i_{C}\left( \left. 0 \right.\_ \right)}}}{2\beta L_{C}}} \\ {{\alpha = {- \frac{R_{C}}{2L_{C}}}},} & {\beta = \frac{\sqrt{R_{C}^{2} - \frac{4L_{C}}{C}}}{2L_{C}}} \end{matrix} \right. & (3) \end{matrix}$

It can be seen from equations (2) and (3) that the magnitude of the charging current i_(C) is influenced by the charging resistor and the charging inductor.

2) Fault Isolation Stage

The fault isolation stage refers to the whole process from fault occurrence to isolation, and the specific process is described as follows:

At time t₀, a fault occurs, and fault current flows from the converter stations to a fault point through the low-loss branch, in the meantime, the preliminary current limiting link is started immediately to preliminarily limit the rise of the fault current, and an instruction is given to block the IGBT device and turn on the thyristor T₀ to allow the fault current on the steady-state low-loss branch to be quickly transferred to the transfer branch; and the disconnector UFD₁ can be turned off when the current flowing through the disconnector UFD₁ drops to 0.

FIG. 5 shows an equivalent circuit at the preliminary current limiting stage in case of a fault, R_(eq) and L_(eq) are equivalent resistance and equivalent inductance of the converter station, where R_(eq)=2R_(arm)/3 and L_(eq)=2L_(arm)/3, L_(dc) is the current limiting inductor disposed on the line, and R_(L) and L_(L) are equivalent resistance and equivalent inductance of the DC line between the fault point and the current limiting inductor, respectively.

With preliminary current limiting control, the voltage of each bridge arm needs to be multiplied by the voltage regulation coefficient K, so the sum of voltage of the sub-modules for the bridge arm units is: u _(p) =KU _(dc)  (4)

The fault current in the preliminary current limiting stage during t₀-t₁ is theoretically calculated. When the preliminary current limiting as shown in FIG. 3 is adopted, the voltage regulation coefficient is:

$\begin{matrix} {K = {1 - {K_{I}\frac{{di}_{dc}}{dt}}}} & (5) \end{matrix}$

Assuming L=L_(eq)+L_(dc)+L_(L) and R=R_(eq)+R_(L), and the initial condition is i_(dc)(t₀)=I_(dc), an equation can be obtained from FIG. 7:

$\begin{matrix} {{\frac{{di}_{dc}}{dt} + {\frac{R}{L + {K_{I}U_{dc}}}i_{dc}}} = \frac{U_{dc}}{L + {K_{I}U_{dc}}}} & (6) \end{matrix}$

the solution is:

$\begin{matrix} {i_{dc} = {{\left( {I_{dc} - \frac{U_{dc}}{R}} \right)e^{\frac{t}{\tau_{dif}}}} + \frac{U_{dc}}{R}}} & (7) \end{matrix}$

where, τ_(dif)=(L+K₁U_(dc))/R is the time constant under preliminary current limiting. At time t₁, assuming i_(dc)(t₁)=I₁.

At time t₁, the fault is detected, the disconnector UFD₁ is turned off, and the thyristor T₁ is turned on, the pre-charging capacitor is connected to the fault current circuit, and the number of control sub-modules of the source-side converters is reduced, so that the sum of voltage of sub-modules for upper and lower bridge arms of the converters is less than the voltage u_(Cflt) of the pre-charging capacitor;

in the process, the fault current in the transfer branch drops to zero at a large rate to turn off the thyristor T₀, and the fault point is isolated after the thyristor T₀ is turned off. The converters then immediately switch from voltage regulation control to a conventional control mode, allowing the DC grid to restore normal operation.

FIG. 6 shows an equivalent circuit in the fault isolation stage. When the converters use the adaptive voltage regulation link as shown in FIG. 3, the voltage regulation coefficient K satisfies the following equation:

$\begin{matrix} {K = {K_{rel}\frac{u_{Cflt}}{U_{dc}}}} & (8) \end{matrix}$

Based on equation (8), the sum of voltage of the sub-modules for the bridge arm units is: u _(p) =K _(m) U _(dc) =K _(rel) u _(Cflt)  (9)

The fault current and capacitor voltage in the source-grid coordination stage during t₁-t₂ are calculated theoretically, and the initial conditions are i_(dc1)(t₁)=i_(dc2)(t₁)=I₁, u_(Cflt)(t₁)=U_(dc), then the following equation can be obtained from FIG. 8:

$\begin{matrix} {\begin{pmatrix} \frac{{du}_{Cflt}}{dt} \\ \frac{{di}_{del}}{dt} \\ \frac{{di}_{{dc}2}}{dt} \end{pmatrix} = {\begin{pmatrix} 0 & \frac{1}{C} & {- \frac{1}{C}} \\ \frac{K_{rel} - 1}{L_{eq}} & {- \frac{R_{eq}}{L_{eq}}} & 0 \\ \frac{1}{L_{dc} + L_{L}} & 0 & {- \frac{R_{L}}{L_{dc} + L_{L}}} \end{pmatrix}\begin{pmatrix} u_{Cflt} \\ i_{{dc}1} \\ i_{{dc}2} \end{pmatrix}}} & (10) \end{matrix}$

It is difficult to get the analytical solution of equation (10) directly, but numerical solutions of u_(Cflt), i_(dc1) and i_(dc2) can be found by the Runge-Kutta method.

According to the numerical solution of equation (10), the fault current i_(dc1) is affected by the voltage u_(Cflt) of the pre-charging capacitor and the equivalent inductance L_(eq) and equivalent resistance R_(eq) of the bridge arms; the voltage u_(Cflt) of the pre-charging capacitor is mainly affected by L_(L), R_(L) and L_(dc), and decrease of the u_(Cflt) is mainly caused by discharge of the pre-charging capacitor to the fault point; and the fault current i_(dc2) is affected by the capacitance C. At time t₂, the i_(dc1) drops to zero, and assuming i_(dc) ²(t₂)=I₂ and u_(Cflt)(t₂)=U₂.

At time t₂, the thyristor T₀ is turned off, energy of the pre-charging capacitor is transferred to the current limiting inductor, and the UFD₂ is turned off to isolate the fault line; after the fault is isolated, the MMC immediately switches from an adaptive voltage regulation control mode to a conventional control mode to restore normal operation of the DC grid.

The fault current and capacitor voltage during t₂-t₃ are calculated theoretically and the initial conditions are u_(C)(t₂)=U₂, i_(C)(t₂)=i_(L)(t₂)=I₂, then the following equation can be obtained from FIG. 7(a):

$\begin{matrix} \left\{ \begin{matrix} {u_{C} = {L_{dc}\frac{{di}_{L}}{dt}}} \\ {{C\frac{{du}_{C}}{dt}} = {{- i_{C}} = {- i_{L}}}} \end{matrix} \right. & (11) \end{matrix}$

the solution is: i _(C) =D ₁ cos(βt)+D ₂ sin(βt)  (12)

where:

$\begin{matrix} \left\{ \begin{matrix} {{D_{1} = I_{2}},} & {D_{2} = \frac{U_{C2}}{\beta L_{dc}}} \\ {\beta = \frac{1}{\sqrt{L_{dc}C}}} &  \end{matrix} \right. & (13) \end{matrix}$

{circle around (1)} At time t₃, the u_(Cflt) drops to zero, the i_(C) and the i_(L) reach the maximum values, and assuming i_(C)(t₃)=i_(L)(t₃)=I₃.

3) Energy Dissipation Stage

The energy dissipation stage refers to the dissipation process of residual energy of the pre-charging capacitor and the line current limiting inductor, the process together with the current limiting isolation stage forms a complete fault clearing process.

At time t₃, the pre-charging capacitor is reversely charged, and the i_(C) and the i_(L) start to decrease, in the meantime, the diode in the energy dissipation branch is turned on, the i_(D) starts to rise from zero, energy of the current limiting inductor L_(dc) is released to the energy dissipation branch, and the pre-charging capacitor is reversely charged.

The fault current and capacitor voltage during t₃-t₄ are calculated theoretically and the initial conditions are u_(C)(t₃)=0, i_(C)(t₃)=i_(L)(t₃)=I₃, i_(D)(t₃)=0, then the following equation can be obtained from FIG. 7(b):

$\begin{matrix} \left\{ \begin{matrix} {u_{C} = {{L_{dc}\frac{{di}_{L}}{dt}} = {R_{e}\left( {i_{C} - i_{L}} \right)}}} \\ {{C\frac{{du}_{C}}{dt}} = {- i_{C}}} \end{matrix} \right. & (14) \end{matrix}$

the solution is:

$\begin{matrix} \left\{ \begin{matrix} {i_{L} = {{D_{1}e^{\alpha t}{\cos\left( {\beta t} \right)}} + {D_{2}e^{\alpha t}{\sin\left( {\beta t} \right)}}}} \\ {u_{C} = {L_{dc}{e^{\alpha t}\left\lbrack {{\left( {{\alpha D_{1}} + {\beta D_{2}}} \right){\cos\left( {\beta t} \right)}} + {\left( {{\alpha D_{2}} - {\beta D_{1}}} \right){\sin\left( {\beta t} \right)}}} \right\rbrack}}} \end{matrix} \right. & (15) \end{matrix}$

where:

$\begin{matrix} \left\{ \begin{matrix} {{D_{1} = I_{3}},} & {D_{2} = {{- \frac{\alpha}{\beta}}I_{3}}} \\ {{\alpha = {- \frac{1}{2{RC}}}},} & {\beta = \frac{\sqrt{\frac{4}{L_{dc}C} - \left( \frac{1}{RC} \right)^{2}}}{2}} \end{matrix} \right. & (16) \end{matrix}$

energy dissipated in the current limiting inductor is:

$\begin{matrix} {W_{L1} = {\int_{t_{4}}^{t_{3}}{\frac{1}{2}L_{dc}{i_{L}^{2}(t)}{dt}}}} & (17) \end{matrix}$

The total energy absorbed by the pre-charging capacitor is:

$\begin{matrix} {W_{C} = {\int_{t_{4}}^{t_{3}}{\frac{1}{2}{{Cu}_{C}^{2}(t)}{dt}}}} & (18) \end{matrix}$

At time t₄, the current i_(C) drops to zero, and assuming i_(L)(t₄)=i_(D)(t₄)=I₄.

At time t₄, the i_(C) drops to zero, the thyristor T₁ is turned off, and the i_(D) reaches the maximum value and starts to decrease; and residual energy of the current limiting inductor L_(dc) is gradually released to the energy dissipation branch.

The inductor current during t₄-t₅ is calculated theoretically and the initial condition is i_(L)(t₄)=i_(D)(t₄)=I₄, then the following equation can be obtained from FIG. 7(c):

$\begin{matrix} {{\frac{di_{L}}{dt} + {\frac{R_{e}}{L_{dc}}i_{L}}} = 0} & (19) \end{matrix}$

the solution is:

$\begin{matrix} {i_{L} = {I_{4}e^{{- \frac{R_{e}}{L}}t}}} & (20) \end{matrix}$

energy dissipated in the current limiting inductor is:

$\begin{matrix} {W_{L\; 2} = {\int_{t_{5}}^{t_{4}}{\frac{1}{2}L_{dc}{i_{L}^{2}(t)}{dt}}}} & (21) \end{matrix}$

{circle around (3)} At time t₅, energy dissipation is over and the fault clearing is completed. The design of element parameters involved in the invention is described as follows:

1) Selection of Coefficients for Source-Side Voltage Regulation Controller

{circle around (1)} Differential coefficient K₁

It can be seen from equation (5) that in the preliminary current limiting stage, the voltage regulation coefficient K is determined by change rate of fault current and differential coefficient. Because the protection device has not yet determined whether the fault is detected when the primary current limiting link works, the voltage regulation coefficient when the primary current limiting link works should be greater than or equal to the voltage regulation coefficient when the adaptive voltage regulation link works. At the moment when the source-grid coordination stage is put into operation, K=K_(rel), so the minimum value of the voltage regulation coefficient in the preliminary current limiting stage is K_(rel), that is, the value range of K is [K_(rel), 1] in the preliminary current limiting stage. Considering the maximum change rate of fault current (di_(dc)/dt)_(max) under the most severe fault, setting calculation can be carried out by the following equation:

$\begin{matrix} {K_{I} = \frac{1 - K_{rel}}{\left( {d{i/d}t} \right)_{\max}}} & (22) \end{matrix}$

In the equation, the change rate of fault current di_(dc)/dt reaches the maximum at the moment of short circuit, and assuming that the DC voltage of the MMC at the moment is U_(dc), the following equation can be obtained from FIG. 2:

$\begin{matrix} {{\frac{di_{dc}}{dt} + {\frac{R_{eq}}{L_{eq} + L_{dc}}i_{dc}}} = \frac{U_{dc}}{L_{eq} + L_{dc}}} & (23) \end{matrix}$

According to equation (23), the maximum change rate of fault current can be solved as follows:

$\begin{matrix} {\left( \frac{di_{dc}}{dt} \right)_{\max} = {{- \frac{R_{eq}}{L_{eq} + L_{dc}}}\left( {I_{dc} - \frac{U_{dc}}{R_{eq}}} \right)}} & (24) \end{matrix}$

Reliability coefficient K_(rel)

It can be seen from equation (8) that the voltage regulation coefficient K is determined by the voltage of the pre-charging capacitor and the reliability coefficient in the source-grid coordination stage. If bridge arm resistance is ignored, voltage on the bridge arm inductor is: u _(L) =U _(Cflt) −u _(p)=(1−K _(rel))u _(Cflt)  (25)

Then the drop rate of current at the head end of the fault line is:

$\begin{matrix} {\frac{{di}_{dcl}}{dt} = {{- \frac{u_{L}}{L_{eq}}} = {- \frac{\left( {1 - K_{rel}} \right)u_{Cflt}}{L_{eq}}}}} & (26) \end{matrix}$

The current at the head end of the fault line is

$\begin{matrix} {{i_{dcl}(t)} = {{I_{1} - {\frac{1}{L_{eq}}{\int_{t_{1}}^{t}{{u_{L}(t)}dt}}}} = {I_{1} - {\frac{1 - K_{rel}}{L_{eq}}{\int_{t_{1}}^{t}{{u_{Cflt}(t)}{dt}}}}}}} & (27) \end{matrix}$

It can be seen from equations (26) and (27) that the drop speed and drop time of the fault current are related to the reliability coefficient K_(rel) and the voltage u_(Cflt) of the pre-charging capacitor, while the reliability coefficient should ensure that the fault current has a sufficient drop rate, and the drop rate of the fault current determines the time from the occurrence of the fault until the fault current is turned off.

Considering the above factors, the reliability coefficient K_(rel) can be selected as 0.8 in a 500 kV DC grid.

2) Parameters for Components in the Transfer Branch

In the system fault detection stage, the thyristor T₀ is on, and I_(T0_max) is used to represent the maximum fault current flowing through the thyristor T₀. After the system detects the fault and turns off the thyristor T₀, the thyristor T₀ needs to withstand a reverse voltage before the disconnector UFD₂ is turned on. Assuming that the maximum reverse voltage on the thyristor T₀ after breaking is U_(T0_max), and U_(T0) and I_(T0) represent rated voltage and rated current of thyristors in the transfer branch respectively, the number of thyristors required in the transfer branch can be calculated by equation (28).

$\begin{matrix} {n_{T\; 0} = {\frac{U_{T\; 0{\_ max}}}{U_{T\; 0}}\frac{I_{T\; 0{\_ max}}}{I_{T\; 0}}}} & (28) \end{matrix}$

3) Parameters for Components in the Discharging Branch

After the fault is isolated, the line-side fault current continues to increase. It can be seen from equation (10) that the maximum fault current is closely related to the capacitance of the pre-charging capacitor, and the maximum line fault current after the fault is isolated can be adjusted by designing the capacitance parameter. Considering the maximum current allowed to pass through the line in the energy dissipation stage, the following equation can be obtained based on Formula (12):

$\begin{matrix} {{I_{dc\_ max} > {{D_{1}{\cos\left( {\beta\; t} \right)}} + {D_{2}{\sin\left( {\beta\; t} \right)}}}} = {{I_{2}{\cos\left( {\frac{1}{\sqrt{L_{dc}C}}t} \right)}} + {U_{C2}\sqrt{\frac{C}{L_{dc}}}{\sin\left( {\frac{1}{\sqrt{L_{dc}C}}t} \right)}}}} & (29) \end{matrix}$

where I_(dc_max) indicates the maximum current allowed to pass through the line.

In addition, in the source-grid coordination stage, too fast voltage drop on the pre-charging capacitor will lead to excessive sub-modules to be removed, which is not good for the stability of the system, so a lower limit is to be set for the pre-charging capacitor C.

Assuming that the minimum number of sub-modules for the single-phase bridge arm during a fault is N_(SM_min), and the corresponding voltage regulation coefficient is K_(min), the following equation can be obtained based on equation (8):

$\begin{matrix} {u_{Cflt} > {\frac{K_{\min}}{K_{rel}}U_{dc}}} & (30) \end{matrix}$

Therefore, the value range of capacitance is determined by equations (29) and (30).

The maximum voltage to be withstood after the thyristor T₁ is turned off is the maximum reverse voltage U_(T1_max) provided after the pre-charging capacitor is reversely charged. The rated voltage of the thyristor T₁ in the discharging branch is denoted by U_(T1) and the rated current of the thyristor T₁ in the transfer branch is denoted by I_(T1), then the number of thyristors required in the discharging branch can be calculated by equation (31).

$\begin{matrix} {n_{T1} = {\frac{U_{T1{\_ max}}}{U_{T0}}\frac{I_{T\; 1{\_ max}}}{I_{T1}}}} & (31) \end{matrix}$

4) Parameters for Components in the Flyback Energy Dissipation Branch

The maximum current of the flyback energy dissipation branch is denoted by I_(D_max), and the maximum reverse voltage withstood by the flyback diode D in the flyback energy dissipation branch is the rated DC voltage U_(dc), U_(D) and I_(D) represent the rated voltage and rated current of the diode D in the flyback energy dissipation branch respectively, then the number of diodes required in the flyback energy dissipation branch can be calculated by equation (32).

$\begin{matrix} {n_{D} = {\frac{U_{dc}}{U_{D}}\frac{I_{D\_ max}}{I_{D}}}} & (32) \end{matrix}$

The size of the energy dissipation resistor determines the duration of releasing the residual energy of the L_(dc) to the energy dissipation branch, τ_(max) represents the maximum time constant allowed for residual energy dissipation of the current limiting inductor, then the value range of the energy dissipation resistor R_(e) is determined by equation (31).

$\begin{matrix} {\frac{L_{dc}}{R_{e}} < \tau_{\max}} & (33) \end{matrix}$

According to the invention, decoupling of fault isolation and fault energy dissipation is realized, with energy dissipation after isolation, fast isolation and slow energy dissipation, thereby greatly improving the speed of fault isolation, so the adaptive fault clearing scheme is applicable to some working conditions with requirement for rapidity.

The above description is only illustrative of preferred embodiments of the invention. It should be noted that those of ordinary skill in the art can make a plurality of improvements and modifications to the invention without departing from the principle of the invention, and these improvements and modifications should fall within the protection scope of the invention. 

What is claimed is:
 1. An adaptive fault clearing scheme for a MMC VSC-HVDC grid based on source-grid coordination, wherein the MMC VSC-HVDC grid comprises two source-side converter stations MMC1 and MMC3, two grid-side converter stations MMC2 and MMC4, wherein converters of the four converter stations are connected in a square shape by double-circuit DC overhead lines, and each converter station is equipped with two converters; a grid-side circuit breaker is disposed at each end of each DC line connected with the converters to coordinate with a source-side control strategy when a fault occurs to the DC line so as to isolate the fault together; the grid-side circuit breaker topology comprises: a steady-state low-loss branch, comprising a disconnector UFD₁, an IGBT device and a disconnector UFD₂ sequentially connected in series; a transfer branch, comprising a thyristor T₀ disposed in parallel, wherein one end of the thyristor T₀ is connected with a front end of the disconnector UFD₁, and other end is connected to a line between the IGBT device and the disconnector UFD₂; a charging circuit, disposed at a rear ends of the steady-state low-loss branch and the transfer branch and formed by sequentially connecting a pre-charging capacitor C, a switch RCB, a charging resistor R_(C) and a charging inductor L_(C) in series; wherein one end of the pre-charging capacitor C is connected with a rear end of the disconnector UFD₂, and one end of the charging inductor L_(C) is grounded; a discharging branch, comprising a thyristor T₁ connected in parallel with the charging circuit, wherein one end of the thyristor T₁ is connected to a ground terminal of the charging inductor L_(C), and other end is connected to a line between the pre-charging capacitor C and the switch RCB; and a flyback energy dissipation branch, connected in parallel with the charging circuit and disposed at a rear ends of the charging circuit and the discharging circuit, and comprising a flyback diode D and an energy dissipation resistor R_(e) connected in series; wherein other end of the energy dissipation resistor R_(e) is grounded, and other end of the flyback diode D is connected with the rear end of the disconnector UFD₂ and a front end of a current limiting inductor L_(dc) disposed at a terminal; wherein the source-side control strategy is realized by a voltage regulation controller; when a system runs stably, the voltage regulation controller does not actuate, and an output voltage regulation coefficient K is kept at 1; after a fault occurs, the voltage regulation controller is started, and the output voltage regulation coefficient K decreases within the range of [0,1], so that voltage at outlets of the converters drops accordingly, and coordinates with voltage of the pre-charging capacitor of the grid-side circuit breaker topology to realize fault isolation based on the source-grid coordination; wherein the voltage regulation controller gives corresponding voltage regulation coefficients Kat different stages after the fault occurs, and the voltage regulation controller comprises a preliminary current limiting link and an adaptive voltage regulation link; the preliminary current limiting link is put into operation until the system detects the fault, while the adaptive voltage regulation link is put into operation only after the system detects the fault; after the fault occurs, the preliminary current limiting link is started immediately to preliminarily limit the development of fault current; after monitoring the fault, a DC grid protection system switches to the adaptive voltage regulation link, and adaptively coordinates with voltage of the grid-side pre-charging capacitor to isolate the fault together.
 2. The adaptive fault clearing scheme for the MMC VSC-HVDC grid based on the source-grid coordination according to claim 1, wherein the pre-charging capacitor C needs to be charged during normal operation of the DC grid, so that the pre-charging capacitor C has a rated DC voltage after charging to lower an output voltage of the voltage regulation controller by adjusting a number of sub-modules for the converters in a fault isolation stage, and coordinate with the voltage of the pre-charging capacitor C to decrease and turn off the fault current.
 3. The adaptive fault clearing scheme for the MMC VSC-HVDC grid based on the source-grid coordination according to claim 1, wherein a voltage attenuation speed of the pre-charging capacitor C is different at different transition resistance when a fault occurs to the DC grid, and the voltage regulation coefficient K is matched with different transition resistance to adaptively adjust a number of removed sub-modules to cope with both metallic short-circuit faults and high-resistance short-circuit faults.
 4. The adaptive fault clearing scheme for the MMC VSC-HVDC grid based on the source-grid coordination according to claim 3, wherein when the fault occurs to the DC grid, fault clearing is achieved by the following steps: at time t₀, the fault occurs, and the fault current flows from the converter stations to a fault point through the steady-state low-loss branch, in the meantime, the preliminary current limiting link is started immediately to preliminarily limit the rise of the fault current, and an instruction is given to block the IGBT device and turn on the thyristor T₀ to allow the fault current on the steady-state low-loss branch to be quickly transferred to the transfer branch; and the disconnector UFD₁ is turned off when a current flowing through the disconnector UFD₁ drops to 0; at time t₁, the fault is detected, the disconnector UFD₁ is turned off, and the thyristor T₁ is turned on, the pre-charging capacitor C is connected to the discharge branch, and a number of control sub-modules of a source-side converters is reduced, so that the sum of voltage of sub-modules for upper and lower bridge arms of the converters is less than a voltage u_(Cflt) of the pre-charging capacitor; in the process, the fault current in the transfer branch drops to zero at a large rate to turn off the thyristor T₀, and the fault point is isolated after the thyristor T₀ is turned off; at time t₂, the thyristor T₀ is turned off, energy of the pre-charging capacitor C is transferred to the current limiting inductor L_(dc), and the disconnector UFD₂ is turned off to isolate a fault line; after the fault is isolated, a MMC switches from an adaptive voltage regulation control mode to a conventional control mode to restore normal operation of the DC grid; at time t₃, the pre-charging capacitor C is reversely charged, and a current i_(C) of the charging circuit and a current i_(L) of the current limiting inductor L_(dc) start to decrease, in the meantime, the diode D in the flyback energy dissipation branch is turned on, a current i_(D) of the diode D starts to rise from zero, energy of the current limiting inductor L_(dc) is released to the flyback energy dissipation branch, and the pre-charging capacitor C is reversely charged; at time t₄, the current i_(C) of the charging circuit drops to zero, the thyristor T₁ is turned off, and the current i_(D) of the diode D reaches a maximum value and starts to decrease; and residual energy of the current limiting inductor L_(dc) is gradually released to the flyback energy dissipation branch; and at time t₅, energy dissipation is over and the fault clearing is completed. 